\\ Pari/GP code for working with elliptic curve 2.2.76.1-121.1-d3
\\ (Note that not all these functions may be available, and some may take a long time to execute.)
\\ Define the base number field:
K = nfinit(a^2 - 19);
\\ Define the curve:
E = ellinit([0, -1, 1, 0, 0],K)
\\ Compute the discriminant:
E.disc
\\ Compute the norm of the discriminant:
norm(E.disc)
\\ Compute the j-invariant:
E.j
\\ Compute the torsion subgroup:
T = elltors(E); T[2]
\\ Compute the order of the torsion subgroup:
T[3]
\\ Compute the generators of the torsion subgroup:
T[3]